Modeling efficiency over a range of velocities in underwater vehicles

ABSTRACT

A method of generating a model of propulsive efficiency for an autonomous underwater vehicle (AUV) is based on a multilayer perception neural network model using data from aquatic species, such as undulatory fin propulsion in the knifefish ( Xenomystus nigri ), and a sensitivity analysis is used to lower the number of required inputs. The model of propulsive efficiency allows an AUV to achieve high values of propulsive efficiency over a range of forward velocity, giving a lowered energy drain on the battery. In an embodiment, externally monitored information, such as that on flow velocity, is conveyed to an apparatus residing in the vehicle&#39;s control unit, which in turn signals the locomotive unit to adopt kinematics, such as fin frequency and amplitude, associated with optimal propulsion efficiency. Power savings could protract vehicle operational life and/or provide more power to other functions, such as communications.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/222,059, filed on Jun. 30, 2009, which is incorporated herein byreference. This application is related to co-pending application Ser.No. 12/824,184, filed on Jun. 27, 2010, entitled “Underwater VehiclesWith Improved Efficiency Over A Range Of Velocities” and to co-pendingapplication Ser. No. 12/824,186, filed on Jun. 27, 2010, entitled“Underwater Vehicles With Propulsive Systems Using Undulatory Fins,”both of which are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to underwater vehicles, and morespecifically to methods and systems that lead to increased propulsiveefficiency of autonomous underwater vehicles (AUVs) over a range ofvelocities.

BACKGROUND

Much research and development on autonomous underwater vehicles (AUVs)has focused on larger vehicles driven by propellers (see for example“Trends in Biorobotic Autonomous Undersea Vehicles,” IEEE Journal ofOceanic Engineering, Vol. 30, No. 1, pp. 109-139, January 2005 by P. R.Bandyopadhyay, incorporated herein by reference).

Research and development has also focused on vehicles with undulatorybody motions (see for example “An Efficient Swimming Machine,”Scientific American, Vol. 272, Issue 3, pp. 64-70, March 1995 by M. S.Triantafyllou et al., “The Geometric Mechanics of Undulatory RoboticLocomotion,” The International Journal of Robotics Research, Vol. 17,No. 7, pp. 683-701, July 1998 by J. Ostrowski et al., “Hydrodynamics ofFishlike Swimming,” Annual Review of Fluid Mechanics, Vol. 32, pp.33-53, 2000 by M. S. Triantafyllou et al., “Nonlinear Control Methodsfor Planar Carangiform Robot Fish Locomotion,” Proceedings of the 2001IEEE International Conference on Robotics and Automation, pp. 427-434,2001 by K. A. Morgansen et al., and “Design and Dynamic Analysis of FishRobot: PoTuna,” Proceedings of the 2004 IEEE International Conference onRobotics and Automation, pp. 4887-4892, April 2004 by E. Kim et al.,each of which is incorporated herein by reference).

More recently, developments in the design and propulsion of biomimeticautonomous underwater vehicles (AUVs) have focused on boxfish as models(see for example “Biomimetric Micro Underwater Vehicle with OscillatingFin Propulsion: System Design and Force Measurement,” Proceedings of the2005 IEEE International Conference on Robotics and Automation, pp.3312-3317, April 2005 by X. Deng et al., incorporated herein byreference). In this paper a biomimetic system concept design,fabrication details and experimental force measurements on prototypeboxfish-inspired vehicles are presented.

While swimming mechanics in boxfish are well understood (e.g. routineswimming performance, maneuverability and stability, carapacehydrodynamics, drag and lift, and vortical flow self-correcting forces),little attention has been given to the functional design and operationof boxfish-inspired vehicles (see for example “Does A Rigid Body LimitManeuverability?,” The Journal of Experimental Biology, Vol. 203, pp.3391-3396, 2000 by J. A. Walker, “Boxfishes and UnusuallyWell-Controlled Autonomous Underwater Vehicles,” Physiological andBiological Zoology, Vol. 73, No. 6, pp. 663-671, 2000 by M. S. Gordon etal., “Boxfishes (Teleoste: Ostraciidae) As A Model System For FishesSwimming With Many Fins: Kinematics,” The Journal of ExperimentalBiology, Vol. 204, pp. 1459-1471, 2001 by J. R. Hove et al., “FishFunctional Design and Swimming Performance,” Journal of Fish Biology,Vol. 65, pp. 1193-1222, 2004 by R. W. Blake, and “Evidence ofSelf-Correcting Spiral Flows in Swimming Boxfishes,” Bioinspiration &Biomimetrics, Vol. 3, 2008 by I. K. Bartol et al., each of which isincorporated herein by reference).

In particular, while boxfish-inspired vehicles have many potentialadvantages in operating in complex environments (e.g. highmaneuverability and stability), limited battery life and payloadcapacities are likely functional disadvantages. In particular, boxfishemploy undulatory median and paired fins during routine swimming whichare characterized by high hydromechanical Froude efficiencies (≈0.9) atlow forward speeds. However, current boxfish-inspired vehicles arepropelled by a low aspect ratio, ‘plate-like’caudal fin (ostraciiformtail) which can be shown to operate at a relatively low maximum Froudeefficiency (≈0.5) and is mainly employed as a rudder for steering and inrapid swimming bouts (e.g. escape responses).

BRIEF SUMMARY OF THE INVENTION

A method of generating a model of propulsive efficiency for anautonomous underwater vehicle (AUV) is based on a multilayer perceptionneural network model using data from aquatic species, such as undulatoryfin propulsion in the knifefish (Xenomystus nigri), and a sensitivityanalysis is used to lower the number of required inputs. The model ofpropulsive efficiency allows an AUV to achieve high values of propulsiveefficiency over a range of forward velocity, giving a lowered energydrain on the battery. In an embodiment, externally monitoredinformation, such as that on flow velocity, is conveyed to an apparatusresiding in the vehicle's control unit, which in turn signals thelocomotive unit to adopt kinematics, such as fin frequency andamplitude, associated with optimal propulsion efficiency. Power savingscould protract vehicle operational life and/or provide more power toother functions, such as communications.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the result of a sensitivity analysis of propulsiveefficiency to different parameters.

FIG. 2 illustrates a model of propulsive efficiency as a function of twoparameters.

FIG. 3 illustrates an apparatus for computing efficiency as a functionof two parameters.

FIG. 4A illustrates an apparatus for computing a parameter as a functionof efficiency and a second parameter.

FIG. 4B illustrates an apparatus for computing a parameter as a functionof efficiency and a second parameter.

DETAILED DESCRIPTION

A neural network model is used to develop a model of propulsiveefficiency over a range of flow velocities. In an underwater vehicle,control unit circuitry is designed using this model to optimizepropulsive efficiency relative to flow velocity. External informationfrom a sensory system on flow velocity sends information to a controlunit including a CPU that in turn sends control signals to a locomotiveunit allowing actuators to operate at maximum efficiency relative toperceived flow conditions. Improving propulsive efficiency results insaving battery power that could protract vehicle life allow for a largerpayload or provide additional power for other functions, such ascommunications. In an embodiment, a vehicle utilizing the model ofpropulsive efficiency has a substantially rigid structure, has anundulatory fin based propulsion system and is an autonomous underwatervehicle (AUV). In alternative embodiments, other vehicle body structurescould be used, other types of propulsive systems could be used, and thevehicle could be under remote control rather than being autonomous.

In an experimental design, three circuit modules have been design basedon multilayer perception neural network models of the hydrodynamicefficiencies of swimming in the knifefish (Xenomystus nigri) (see“Evaluation Using Multilayer Perception Neural Networks: A Case Study ofUndulatory Median Fin Swimming in the Knifefish Xenomystus Nigri,”Journal of Fish Biology, Vol. 71, pp. 1203-1207, 2007 by Li et al.,incorporated herein by reference).

Specifically, a neural network model was implemented into circuitry by(1) construction of networks with the optimal topology based onexperimental data; (2) sensitivity analysis of determinant factors forthe Froude efficiency η_(p) (i.e. forward velocity U, fin lateralvelocity W=∂h/∂t where h is the distance displaced by the fin's trailingedge, and lateral velocity of pushing on the waterw=(∂h∂t⁻¹)+U(∂h∂x⁻¹)); (3) validation and testing of network predictionsand (4) implementation of the neural network into three circuit modules.

Neural Network Model

Neural networks are characterized by distinct topologies of nonlineardifferentiable activation functions in neurons consisting of input,output and hidden layers such that each neuron of a layer is connectedto all others in the next layer (see for example “A Logical Calculus ofthe Ideas Immanent in Nervous Activity,” Bulletin of MathematicalBiology, Vol. 52, No. 1/2, pp. 99-115, 1990, reprinted from 1943, by W.W. McCulloch et al.).

Following the work presented in Li et al. (2007), the optimal neuralnetwork configuration was adopted from a neighborhood of 1-3 layers of1-10 neurons. The momentum learning method was used, which is anadvanced adaptive patterning learning technique progressed from theclassic gradient descent method (see for example. “Electric Utility CoalQuality Analysis Using Artificial Neural Network Techniques,”Neurocomputing, Vol. 23, pp. 195-206, 1998 by H. Salehfar et al.).

Gradient descent incorporates an error back prorogation algorithm totrain weights (based on local information) for minimizing overall error.The instantaneous error of neuron i at the nth training iteration is:e _(i)(n)=d _(i)(n)=y _(i)(n)

where e_(i)(n) is the instantaneous error, d_(i)(n) is the desiredoutput and y_(i)(n) is the neuron output (see for example “Modelling theEffect of Carbon Content on Hot Strength Steels Using a ModifiedArtificial Neural Network,” ISIJ International, Vol. 38, No. 10, pp.1121-1129, 1998 by L. X. Kong et al.).

Weights are trained from the iteration n+1 in gradient descent:W _(ij)(n+1)=W _(ij)(n)+γδ_(i)(n)x _(j)(n)

where W_(ij)(n) is the weight between nodes i and j at iteration n,x_(j)(n) is the present input, δ_(i)(n) is the local gradient whichpointed to the required change in the weight and γ is the learning rate.This method was improved by incorporating ‘momentum learning’ todecrease noise and increase convergence using:

_(ij)(n+1)=W _(ij)(n+1)+α(W _(ij)(n)−W _(ij)(n−1))

where

_(ij)(n+1) and W_(ij)(n) are the weights between nodes i and j atiteration n for momentum learning and gradient descent respectively andα is the momentum factor.

The stopping criterion was chosen at maximum epoch (iterations throughthe patterns represented in the input) of 1000 and at a mean squareerror (MSE)≦0.01:

${MSE} = \frac{\sum\limits_{j = 0}^{p}\;{\sum\limits_{i = 0}^{m}\;\left( {d_{ij} - y_{ij}} \right)^{2}}}{m \cdot p}$

where m is the size of the training dataset, p is the total number ofneurons and y_(ij) and d_(ij) are the network and desired output fordata series i at neuron j respectively.

Input data for analysis of the fin motions of the knifefish (Xenomystusnigri) are derived from a simplified bulk momentum approach based onelongated body theory (see for example “Hydromechanics of Aquatic AnimalPropulsion,” Annual Review of Fluid Mechanics, Vol. 1, pp. 413-446, 1969by M. J. Lighthill, incorporated herein by reference).

In this approach, the mean thrust power P is given by subtracting themean rate at which kinetic energy is wasted in the wake P_(k) from thetotal mean rate of working P_(l) .P = P _(l) − P _(k) =U( MwW )−0.5U( Mw ² )

where M is the added mass at the trailing edge of the undulatory analfin:

$M = {\frac{1}{4}\pi\;\rho\; d_{s}^{2}\beta}$

where ρ, d_(s) and β are water density, the depth of a propulsivesection and the shape factor respectively. The shape factor β isconsidered to be approximately equal to 1 (see for example “AquaticAnimal Propulsion of High Hydromechanical Efficiency,” Journal of FluidMechanics, Vol. 44, Part 2, pp. 265-301, 1970 by M. J. Lighthill,incorporated herein by reference).

The propulsive efficiency η_(p) is given by:η_(p)=1−( P _(l) − P )/ P _(l)

The values for W, w, P, P_(l) , P_(k) and η_(p) as a function of theswimming velocity U were taken from Table 1 of “Swimming in the ElectricEels and Knifefishes,” Canadian Journal of Zoology, Vol., 61, pp.1432-1441, 1983 by R. W. Blake, incorporated herein by reference.). Thistable is illustrated below:

U R_(L) U W w

P P _(kin) P _(tot) η_(p) 0.413 6.2 2.75 0.516 0.125 8.62 35.6 6.46 42.00.85 0.306 4.5 2.00 0.390 0.108 5.50 16.5 3.48 19.9 0.83 0.370 5.5 2.460.478 0.115 7.36 27.2 3.74 31.0 0.88 0.333 5.0 2.22 0.433 0.108 6.2220.6 2.96 23.6 0.87 0.260 3.9 1.73 0.369 0.084 4.20 10.92 1.40 12.320.88 0.200 3.0 1.33 0.260 0.069 2.22 4.44 0.74 5.18 0.86 0.178 2.6 1.150.221 0.069 1.96 3.34 0.62 3.96 0.84 0.170 2.55 1.13 0.210 0.068 1.843.12 0.60 3.72 0.84 0.153 2.3 1.02 0.201 0.065 1.66 2.54 0.50 3.04 0.840.150 2.25 1.00 0.191 0.061 1.46 2.20 0.42 2.62 0.84 0.136 2.05 0.910.162 0.053 1.08 1.48 0.28 1.76 0.84 0.133 2.0 0.89 0.153 0.052 1.021.22 0.28 1.50 0.81 0.130 1.95 0.87 0.142 0.052 0.92 1.20 0.26 1.46 0.820.117 1.75 0.78 0.149 0.049 0.94 1.10 0.22 1.50 0.83 0.103 1.55 0.670.127 0.049 0.76 0.78 0.18 0.98 0.80 0.094 1.41 0.63 0.130 0.044 0.720.68 0.14 0.82 0.82 0.090 1.35 0.60 0.131 0.043 0.72 0.66 0.12 0.78 0.830.087 1.30 0.58 0.126 0.044 0.70 0.60 0.12 0.74 0.82 0.085 1.27 0.570.111 0.045 0.60 0.52 0.12 0.64 0.80 0.082 1.23 0.55 0.109 0.044 0.580.46 0.12 0.58 0.78 0.080 1.20 0.53 0.107 0.039 0.52 0.41 0.10 0.52 0.810.079 1.19 0.52 0.103 0.040 0.50 0.40 0.10 0.50 0.80 0.077 1.16 0.510.092 0.039 0.44 0.32 0.08 0.40 0.80 0.076 1.12 0.50 0.083 0.035 0.340.28 0.08 0.34 0.78 0.073 1.11 0.49 0.076 0.037 0.32 0.24 0.08 0.32 0.750.067 1.00 0.45 0.061 0.038 0.24 0.16 0.08 0.24 0.67 0.066 0.91 0.440.058 0.036 0.22 0.14 0.06 0.20 0.70 0.056 0.84 0.37 0.056 0.036 0.200.12 0.06 0.18 0.67Sensitivity Analysis

Sensitivity analysis was performed on the trained neural network todetermine the relative importance of each variable using weights derivedfrom the training process and measuring the change in the predictedoutput for every 50 divisions of 1 SD of the mean input. The optimalityand accuracy was tested based on the cross-validation scheme using 50%of the dataset for training and 50% for MLP-NN performance testing. Thesensitivity analysis showed that the swimming speed U and fin lateralspeed W were the major determinants of η_(p) and this suggested the useof these parameters for implementation into circuitry. In alternativeembodiments, the parameter w could also have been included as an input,as well as other parameters.

FIG. 1 illustrates sensitivity for the predicted efficiency η_(p)(defined as the change in the mean output for every 50 divisions within1 SD of the mean input), swimming speed U, lateral velocity of the finW, lateral velocity of pushing on the water slice w, thrust T, meanthrust power P, kinetic energy wasted in the wake P_(kin) and mean totalpower P_(tot). The numerical results of the sensitivity analysis areshown in the table below:

Parameter Sensitivity to η_(p) U (m s − 1) 0.356122 W (m s − 1) 1.114775w (m s − 1 ) 0.061856 T (×110 − 3N) 0.011263 P (×10 − 4W) 0.000644P_(kin) (×10 − 4W) 0.019360 P_(tot) (×10 − 4W) 0.000158

The neural network model was then constructed based on thecross-validation scheme (75% of the data were used to train the neuralnetwork and 25% was used to test its performance) and good agreement wasfound between neural network predictions and actual values (P>0.05).FIG. 2 shows a three-dimensional representation of the output from thetrained neural network based on U, W and η_(p). The output of thetrained neural network is shown in the table below:

W U 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.05 0.69 0.790.84 0.86 0.86 0.87 0.88 0.88 0.88 0.88 0.10 0.70 0.79 0.83 0.85 0.860.87 0.87 0.88 0.88 0.88 0.15 0.70 0.79 0.83 0.84 0.85 0.86 0.87 0.870.88 0.88 0.20 0.71 0.79 0.82 0.84 0.85 0.86 0.86 0.87 0.87 0.88 0.250.71 0.79 0.81 0.83 0.84 0.85 0.86 0.86 0.87 0.87 0.30 0.72 0.78 0.810.82 0.83 0.84 0.85 0.86 0.86 0.87 0.35 0.73 0.78 0.81 0.82 0.83 0.840.85 0.85 0.86 0.87 0.40 0.74 0.78 0.80 0.81 0.82 0.83 0.84 0.85 0.860.86 0.45 0.74 0.78 0.80 0.81 0.82 0.83 0.84 0.84 0.85 0.86 0.50 0.750.78 0.80 0.80 0.81 0.82 0.83 0.84 0.85 0.85

Experimental Implementation

Three circuit modules were designed: (1) fin lateral speed versusswimming speed giving propulsive efficiency (FIG. 3), (2) propulsiveefficiency versus fin lateral speed giving swimming speed (FIG. 4A) and(3) propulsive efficiency versus swimming speed giving fin lateral speed(FIG. 4B). The experimental implementation (summarized in FIGS. 3, 4Aand 4B and consisting of 1918, 2318 and 2362 gates respectively)utilizes inverters as well as logic circuits of two, three and four6-bit and 7-bit inputs. Each module is composed of combinatorial logicand is activated by two inputs and produces one output. Each modulerepresents the entire array of swimming efficiencies, swim speeds andfin speed efficiencies illustrated in FIG. 2.

In FIG. 3, swimming speed (U) is input at 32 into combinatorial circuit30 and fin lateral speed (W) is input at 34. Propulsive efficiency(η_(p)) is output at 36 from combinatorial circuit 30. In an embodiment,inputs 32 and 34 consist of 6-bit inputs that encode the inputparameters as binary values. Other widths of input and other forms ofencoding the input parameters are possible. In an embodiment, output 36contains an individual signal for each value in the efficiency curve. Inother embodiments, output 36 can be encoded as a binary value. In someembodiments, circuit 30 may be replaced by a sequential circuit or maybe implemented as a software routine in the control unit of a vehicle.In some embodiments interpolation between points on the efficiency curvemay be performed to provide an output for all input values.

In FIG. 4A, fin lateral speed (W) is input at 41 into combinatorialcircuit 40 and propulsive efficiency (η_(p)) is input at 42. Swimmingspeed (U) is output at 43 from combinatorial circuit 40. In anembodiment, inputs 41 and 42 consist of 6-bit and 7-bit inputsrespectively that encode the inputs as binary values. Other widths ofinput and other forms of encoding the inputs are possible. In anembodiment, output 43 contains an individual signal for each value ofswimming speed. In other embodiments, output 43 can be encoded as abinary value. In some embodiments, circuit 40 may be replaced by asequential circuit or may be implemented as a software routine in thecontrol unit of a vehicle. In some embodiments interpolation betweenpoints on the efficiency curve may be performed to provide an output forall input values.

In FIG. 4B, swimming speed (U) is input at 46 into combinatorial circuit45 and propulsive efficiency (η_(p)) is input at 47. Fin lateral speed(W) is output at 48 from combinatorial circuit 45. In an embodiment,inputs 46 and 47 consist of 6-bit and 7-bit inputs respectively thatencode the inputs as binary values. Other widths of input and otherforms of encoding the inputs are possible. In an embodiment, output 48contains an individual signal for each value of fin lateral speed. Inother embodiments, output 48 can be encoded as a binary value. In someembodiments, circuit 45 may be replaced by a sequential circuit or maybe implemented as a software routine in the control unit of a vehicle.In some embodiments interpolation between points on the efficiency curvemay be performed to provide an output for all input values.

A variety of control scenarios are possible with the circuitsillustrated in FIGS. 3, 4A and 4B or with alternative embodiments ofthese circuits. Note that the outputs of circuits 30, 40 and 45 areequal to the results of the neural network model. The values ofpropulsive efficiency are at least 0.69 for all inputs and achieve 0.88at higher forward velocities. By having a model of efficiency over arange of forward velocities, it is possible for the control unit of anunderwater vehicle to utilize such information to improve propulsiveefficiency given the other constraints imposed by the overall system.

SUMMARY

A basic design for the major design units of biomimetic MUVs based onoscillatory propulsion employing a boxfish model are described in Denget al. (2005). In this design, there are five main units: locomotory,sensory, power, communications and control. In this design, the MUV ispropelled by an electromechanical actuated-fin system. Two side fins(for steering and moving upward and downward) and a plate-like caudalfin (ostraciiform tail) for propulsion are driven by a PZT bimorphactuator with motion amplification from four bar mechanisms. The finsare powered by electric energy (e.g. a lithium battery) and the powersupply, communications (e.g. ultrasonic transmitters), sensory (e.g.flow velocity detection) units feed into the control (CPU) unit.

Other types of propulsion system have been studied based on differentbiomimetic models besides the ostraciiform propulsion of the boxfish.For example anguilliform propulsion is described in Ostrowski et al.(1998), carangiform propulsion (where approximately two thirds of thebody undulates) is described in Morgansen et al. (2001), thunniformpropulsion is described in Triantafyllou et al. (1995), incorporatedherein by reference, and an undulatory fin model is described in“Biomimetric Compliant System for Smart Actuator-Driven AquaticPropulsion: Preliminary Results,” Proceedings of 203 ASME InternationalMechanical Engineering Congress & Exposition (IMECE'03), November 2003by B. P. Trease et al., incorporated herein by reference, and“Kinematics and Force Characterization of a Knifefish-InspiredMechanical Propulsor,” Proceedings of Biological Approaches toEngineering Conference, March 2008 by K. Collins et al., incorporatedherein by reference. In the case of undulatory fins, Trease et al.(2003) describes sinusoidally undulating flexible fins with distributedcompliance based on a rib structure and Collins et al. (2008) describessuch a design incorporated into a ‘WaveDrive’ actuating mechanism withpreliminary measurements on thrust production.

Nevertheless, currently the ‘ostraciiform model’ is favored with respectto the design and function of small, highly maneuverable and stable AUVs(see for example Gordon et al. (2000), “Hydrodynamic Stability ofSwimming In Ostraciid Fishes: Role of the Carapace in the SmoothTrunkfish Lactophyrs triqueter (Teleostei: Ostraciidae),” The Journal ofExperimental Biology, Vol. 206, pp. 725-744, 2003 by I. K. Bartol etal., “Fish Functional Design and Swimming Performance,” Journal of FishBiology, Vol. 65, pp. 1193-1222, 2004 by R. W. Blake, and Deng et al.(2005), each of which is incorporated herein by reference).

While these approaches to AUV function have certain advantages as far asbody design, maneuverability and stability are concerned, the currentfocus on an oscillating plate as a basis for propulsion has significantdisadvantages. In particular, it can be shown that the maximum Froudeefficiency of a low aspect ratio ‘plate-like’ caudal fin propeller(ostraciiform tail) has a relatively low upper value of approximately0.5 (see for example “Mechanics of Ostraciiform Propulsion,” CanadianJournal of Zoology, Vol. 59, pp. 1067-1071, 1981 by R. W. Blake). Infact, boxfish are not propelled by the reciprocating motions of theircaudal fin during routine activity. Rather, they swim through the actionof undulatory median and paired fins and, in rectilinear swimming, thecaudal fin is often collapsed presumably to reduce drag. It has beenobserved that the caudal fin is mainly employed as a rudder for steeringand in bouts of unsteady swimming.

A more efficiently propelled underwater vehicle can be achieved by usingan undulatory fin and can use a control unit that utilizes a model ofswimming efficiency over a range of velocities. Undulatory fin basedpropulsion results in increased efficiency over a range of velocitiesand is particularly well adapted to vehicles utilizing low velocitiesand lower power utilization. In an embodiment of such a vehicle, part ofa control unit could be based on the three circuit modules describedabove to optimize propulsive efficiency relative to the flow velocity.External information on flow velocity could be conveyed by sensorsignals to the control unit which in turn could instruct the locomotorunit to appropriately match fin frequency, and hence W, to achieveoptimum propulsive efficiency. Under these conditions, the energy drainon the power unit would be minimized at any given U. This power savingcould protract the operational life of the vehicle and/or provide morepower to other functions such as sensors and communications.

Undulatory median and paired fin swimming is an adaptation forpropulsion for high hydromechanical efficiency at low forward speeds(see for example Blake (2004)). Given that biomimetically inspiredengineering designs need not be constrained by the limitations imposedby phylogenetic (historical) or ontogenetic (developmental) factors,optimal structural and functional solutions can be found by selectingappropriate design features from a variety of ‘fish models’.Specifically, the relatively low drag, high stability andmaneuverability of the boxfish carapace can be combined with anundulatory fin-based propulsion system rather than an oscillating findesign.

The foregoing descriptions of embodiments of the present invention havebeen presented for purposes of illustration and description only. Theyare not intended to be exhaustive or to limit the present invention tothe forms disclosed. Accordingly, many modifications and variations willbe apparent to practitioners skilled in the art. The scope of presentinvention is defined by the appended claims.

The invention claimed is:
 1. A method of determining the propulsiveefficiency of an underwater vehicle in operation comprising the stepsof: providing data representing a plurality of parameters frommeasurements of one or more aquatic species over a variety of swimmingspeeds; training a neural network for propulsive efficiency over a rangeof velocities utilizing said data; computing a sensitivity of one ormore of said parameters to propulsive efficiency; selecting a subset ofsaid parameters based on the results of said step of computing;developing a model of propulsive efficiency utilizing said subset ofsaid parameters; implementing said model of propulsive efficiency in acontrol apparatus; using said control apparatus in real time to computethe propulsive efficiency of an underwater vehicle while in operationover a range of velocities wherein the largest and smallest velocitieshave a ratio of 10 to 1 or greater.
 2. The method of claim 1 whereinsaid step of using comprises the steps of: measuring one or more of saidsubset of parameters from the environment of said underwater vehiclewhile in operation; utilizing the results of said step of measuring tocompute the propulsive efficiency of said underwater vehicle in realtime; controlling a locomotor system of said underwater vehicle based onsaid step of utilizing.
 3. The method of claim 1 wherein said step ofimplementing comprises providing a central processing unit (CPU) coupledto combinatorial circuitry.
 4. The method of claim 1 wherein said stepof implementing comprises providing a central processing unit (CPU) andprogram code.
 5. The method of claim 1 wherein said one or more aquaticspecies comprises a Xenomystus nigri.
 6. The method of claim 1 wheresaid underwater vehicle comprises a substantially rigid structure andsaid locomotor system comprises an undulatory fin propulsion system. 7.The method of claim 1 wherein said subset of parameters includes aforward velocity.
 8. The method of claim 1 wherein said subset ofparameters includes a lateral fin speed.
 9. The method of claim 1wherein said subset of parameters includes a lateral velocity of pushingon the water.
 10. The method of claim 1 wherein said autonomousunderwater vehicle is operated at propulsive efficiencies greater than0.70 over a range of velocities.
 11. The method of claim 1 wherein saidstep of using is performed over a range of velocities of 0.45 meters persecond or greater.
 12. The method of claim 1 wherein said underwatervehicle is an autonomous underwater vehicle (AUV).
 13. The method ofclaim 1 wherein said underwater vehicle is under remote control.